Asian-European Journal of Mathematics

In this attempt, the stability of a connection on Hermitian vector bundles over a Riemannian manifold for the generalized Jensen-type functional equation

In this paper, we introduce a new form of the quadratic reciprocal functional equation. Then, we study the Hyers–Ulam stability for this quadratic reciprocal functional equation in non-Archimedean fields.

It is well-known that the transformation semigroup $T(X)$ is regular, but their subsemigroups need not be. A fence is an ordered set that the order forms a path with alternating orientation. Consider $X$ as the base set of a fence $X=(X;\le )$. Two subsemigroups of $T(X)$ are studied. Namely, the semigroup $DT(X)$ of all order-decreasing self-mappings of $X$ and the semigroup $OT(X)$ of all order-preserving self-mappings of $X$. In this paper, we obtain that $DT(X)$ is a coregular subsemigroup of $T(X)$. A characterization of regular subsemigroups $OT(X)$ of $T(X)$ is given, that is, $OT(X)$ is regular if and only if $\left|X\right|\le 4$. Finally, we discuss the regularity of elements in $OT(X)$.

In this paper, we study the mathematical model proposed by Owen and Sherratt in 1997. We prove that the classical solutions to this model are uniformly-in-time bounded.

Given a holomorphic vector bundle $E$ with a strongly pseudoconvex Finsler metric $F$, an intrinsic approach to complex Finsler geometry as given by Kobayashi is proposed in order to study the negativity of $E$.

We describe a basis of the center of the Schur algebra that comes from conjugacy classes in the symmetric group via Schur–Weyl duality. We give a combinatorial description of expansions of these basis elements in terms of the basis originally used by Schur. The primitive central idempotents of the Schur algebra can be written down using this basis and the character table of the symmetric group in the semisimple case. Along the way we prove a result on the non-singularity of the submatrix of the character table matrix of a symmetric group obtained by taking rows and columns indexed by partitions with at most $n$ parts for any $n$.

Let $X$ be a compact metric space, and let $f:X\to X$ be a homeomorphism. We show that if $f$ has the limit shadowing property then $f$ is chaotic in the sense of Li–Yorke. Moreover, $f$ is dense Li–Yorke chaos.

In this paper, we prove that regular paramedial division groupoids and binary regular paramedial division algebras are linear over an abelian group. Using this results we prove that every finitely generated paramedial division groupoid is a quasigroup and that every paramedial division groupoid is a homomorphic image of a paramedial quasigroup.

Mittal, Rhoades (1999–2001), Mittal et al. (2005, 2006, 2011) have initiated a study of error estimates through trigonometric Fourier approximation (tfa) for the situation in which the summability matrix $T\equiv (a_{n,k})$ does not have monotone rows. Recently Mohanty et al. (2011) have obtained a theorem on the degree of approximation of functions in Besov space $B_q^{\alpha }(L_p)$ by choosing $T$ to be a Nörlund ($N_p$)-matrix with non-increasing weights $\{p_n\}$. In this paper, we continue the work of Mittal et al. and extend the result of Mohanty et al. (2011) to the general matrix $T$.

The set of all pairs of natural numbers is considered as a directed set under the direction: $(m,n)\le (i,j)$ if and only if $m\le i$ and $n\le j$. This directed set is used to study convergence of a double series in a sense of Pringsheim and to introduce double bases in topological vector spaces. An introductory study on double bases is presented.

In this paper, we show if $R$ is a filtered ring then we can define a filtration on $M_n(R)$ which induced by a filtration on $R$, and we prove some properties and relations for $M_n(R)$. Also, we show if $R$ is a filtered ring then we can define a filtration on $D_n(R)$, and we prove some properties and relation for $D_n(R)$. Later we show that, there exist a Dubrovin valuation on $R$, if $R$ is a semisimple ring.

Wavelets have become a powerful tool for having applications in almost all the areas of engineering and science such as numerical simulation of partial differential equations. In this paper, we present the Haar wavelet method (HWM) to solve the linear and nonlinear Klein–Gordon equations which occur in several applied physics fields such as, quantum field theory, fluid dynamics, etc. The fundamental idea of HWM is to convert the Klein–Gordon equations into a group of algebraic equations, which involve a finite number of variables. The examples are given to demonstrate the numerical results obtained by HWM, are compared with already existing numerical method i.e. finite difference method (FDM) and exact solution to confirm the good accuracy of the presented scheme.

A 2-rainbow dominating function (2RDF) of a graph $G$ is a function $f$ from the vertex set $V(G)$ to the set of all subsets of the set $\{1,2\}$ such that for any vertex $v\in V(G)$ with $f(v)=\varnothing$, the condition ${\bigcup }_{u\in N(v)}f(u)=\{1,2\}$ is fulfilled. The weight of a 2RDF $f$ is the value $\omega (f)={\sum }_{v\in V(G)}|f(v)|$. The $2$-rainbow domination number of a graph $G$, denoted by ${\gamma }_{r2}(G)$, is the minimum weight of a 2RDF of $G$. The rainbow bondage number $b_{r2}(G)$ of a graph $G$ with maximum degree at least two is the minimum cardinality of all sets $E^{\prime }\subseteq E(G)$ for which ${\gamma }_{r2}(G-E^{\prime })>{\gamma }_{r2}(G)$. Dehgardi, Sheikholeslami and Volkmann, [The $k$-rainbow bondage number of a graph, Discrete Appl. Math. 174 (2014) 133–139] proved that the rainbow bondage number of a planar graph does not exceed 15. In this paper, we generalize their result for graphs which admit a $2$-cell embedding on a surface with non-negative Euler characteristic.

Let $f:A\to B$ be a ring homomorphism and let $J$ be an ideal of $B$. In this paper, we investigate the transfer of the $(n,d)$-property from a ring $A$ to his amalgamated algebra $A{\bowtie }^{f}J$. Our aim is to give new and original families of $(2,d)$-rings which are neither $(1,d)$-rings ($d=0,1,2$) nor $(2,d-1)$-rings ($d=1,2$), and examples of $(3,d)$-rings which are neither $(2,d)$-rings ($d\ge 0$) nor $(3,d-1)$-rings ($d\ge 1$).

We present a local convergence analysis for the Jarratt-type method of high convergence order in order to approximate a solution of a nonlinear equation in a Banach space. Our sufficient convergence conditions involve only hypotheses on the first Fréchet-derivative of the operator involved. Earlier studies use hypotheses up to the third Fréchet-derivative. Hence, the applicability of these methods is expanded under weaker hypotheses and less computational cost for the constants involved in the convergence analysis. Numerical examples are also provided in this study.

Pseudo-differential operators (p.d.os) involving generalized Hankel–Clifford transformation associated with the symbol $a(x,y)$ whose derivatives satisfy certain growth condition are defined and the Zemanian type function spaces ${ℍ}_{\beta }(I)$ and ${𝕊}_{\alpha }(I)$ are introduced. It is shown that p.d.o’s are continuous linear map of the space ${ℍ}_{\beta }(I)$ and ${𝕊}_{\alpha }(I)$ into itself. Also an Integral representation of p.d.o is obtained.

The es-splitting operation on a $3$-connected binary matroid may not preserve the $3$-connectedness of the matroid. In this paper, we provide a sufficient condition for a $3$-connected binary matroid to yield a $3$-connected binary matroid under the es-splitting operation. We derive a splitting lemma for $3$-connected binary matroids as an application of this result.

A $2$-rainbow dominating function (2RDF) of a graph $G$ is a function $f$ from the vertex set $V(G)$ to the set of all subsets of the set $\{1,2\}$ such that for any vertex $v\in V(G)$ with $f(v)=\varnothing$ the condition ${\bigcup }_{u\in N(v)}f(u)=\{1,2\}$ is fulfilled, where $N(v)$ is the open neighborhood of $v$. The weight of a 2RDF $f$ is the value $\omega (f)={\sum }_{v\in V}|f(v)|$. The $2$-rainbow domination number of a graph $G$, denoted by ${\gamma }_{r2}(G)$, is the minimum weight of a 2RDF of G. The $2$-rainbow domination subdivision number ${\mathrm{\text{sd}}}_{{\gamma }_{r2}}(G)$ is the minimum number of edges that must be subdivided (each edge in $G$ can be subdivided at most once) in order to increase the 2-rainbow domination number. It is conjectured that for any connected graph $G$ of order $n\ge 3$, ${\mathrm{\text{sd}}}_{{\gamma }_{r2}}(G)\le {\gamma }_{r2}(G)$. In this paper, we first prove this conjecture for some classes of graphs and then we prove that for any connected graph $G$ of order $n\ge 3$, ${\mathrm{\text{sd}}}_{{\gamma }_{r2}}(G)\le 2{\gamma }_{r2}(G)-2$.

The cross-correlation of two generalized Boolean functions defined on ${\mathbb{Z}}_2^n$ with values in ${\mathbb{Z}}_q$ is discussed in literature for $q=2^2$. We generalize this result for $q=2^s;$ $s\ge 2$ and show that the existing result is a special case of our work. Further, we give some constructions of gbent functions.

Two main goals are achieved in this article. On the one hand, we introduce the notion of pure ideal in hyperlattices and provide both algebraic and topological characterizations of the notion. On the other hand, we introduce normal hyperlattices, as a natural generalization of normal lattices as treated by Cornish. We obtain both a topological characterization and a characterization in terms of maximal ideals of normal hyperlattices. Finally, we include illustrative examples of pure ideals, normal hyperlattices.

The syntactic semigroup problem is to decide whether a given finite semigroup is syntactic or not. This work investigates the syntactic semigroup problem for both the semigroup reducts of $A^{+}(B_n)$, the affine near-semiring over a Brandt semigroup $B_n$. It is ascertained that both the semigroup reducts of $A^{+}(B_n)$ are syntactic semigroups.

We study ${𝒜}$-Ci modules ($i=2,3$), first introduced in [K. Oshiro, Continuous modules and quasi-continuous modules, Osaka J. Math. 20 (1983) 681–694], and ${𝒜}$-SSP modules. We consider the cases when these classes of modules coincide. As a consequence, we obtain some results related to simple-direct-injective modules. We also investigate some properties of SSP formal matrix rings and describe semiartinian SSP rings.

Let $R$ be a ring equipped with an endomorphism $\alpha$ and an $\alpha$-derivation $\delta$. In this article, we study $(\alpha ,\delta )$-constant Armendariz rings and radicals of the Ore extension $R[x;\alpha ,\delta ]$, in terms of a $(\alpha ,\delta )$-constant Armendariz ring $R$ with an $\alpha$-condition, are determined. We prove that several properties transfer between $R$ and the Ore extension $R[x;\alpha ,\delta ]$, in case $R$ is $\alpha$-compatible $(\alpha ,\delta )$-constant Armendariz.

Let $R$ be a 2, 3-torsion-free prime $(-1,1)$ ring with commutative center $C$. If $C$ is not contained in the nucleus $N$, then a ring defined by a new product $R_{-}:=(R,+,[,])$ is nilpotent of index at most 11.

The notion of a $\sigma$-ideal in a $0$-$1$ distributive lattice is introduced and studied. Certain classes of $0$-$1$ distributive lattices such as normal lattices, complemented lattices, generalized Stone lattices are characterized by using the properties of $\sigma$-ideals. Stable ideals are defined and a necessary and sufficient condition for a $\sigma$-ideal to be stable is given.

Let $F[L]$ be the loop algebra of a loop $L$ over a field $F$. In this paper, we characterize the structure of the unit loop of $F[L]$ modulo its Jacobson radical when $L=M(D_{2m},2)$ is an $RA2$ loop obtained from the dihedral group of order $2m$, $m$ is an odd number and $F$ is a finite field of characteristic $2$. The structure of $1+J(F[L])$ is also determined.

In this paper, we establish a new subfamily ${\wp }_p(\tau ,\alpha ,\beta )$ of multivalent functions with negative coefficients that involve certain linear operator. We first investigate sharp results concerning coefficients, then obtain the distortion theorem, radius of convexity and close-to-convexity, closure theorem, neighborhood property, partial sums and integral representation.

We classify the maximal Clifford inverse subsemigroups $S$ of the full transformation semigroup ${{𝒯}}_n$ on an $n$-element set with $s=s^{-1}$ for all $s\in S$. This classification differs from the already known classifications of Clifford inverse semigroups, it provides an algorithm for its construction. For a given natural number $r\le n$, we find also the largest size of an inverse subsemigroup $S$ of ${{𝒯}}_n$ satisfying $s=s^{-1}$ with least rank $r$ for any element in $S$.